any measure that becomes valued turns into a gamified target

That's a cynical management cliche that every newly-minted MBA seems to repeat. Its real intent is to raise awareness that measures can be gamed. But another MBA cliche with more substance is that you cannot manage what you can't measure (again with the caveat that you might be inadvertently creating incentives to cook the books when you do so). Every business and almost every government organisation rely on metrics and KPIs in order to function, and it's difficult to imagine any system where that's not the case.

I learned thermodynamics before I learned economics, so it didn't escape my notice that GDP looks more like a measure of heat than a measure of work. It gives an overall "operating temperature" of the economy, which is a useful thing to know, but it doesn't tell you what good it's doing you. For example, paying a milion people to dig holes, then fill them back in, would be reflected in GDP. The usefulness of that activity is a separate question. Broken window theory, etc.